The striker completed his transfer from the Rams for an undisclosed fee on Thursday and signed a three-year deal at Fratton Park.
"Once I heard Portsmouth were interested, it was something I couldn't turn down," said the 28-year-old.
"It's exciting times at the club - people I've spoken to have told that it's a club that's going places and it's something I'm really looking forward to."
Pompey started the week with just eight first-team players in pre-season training but manager Steve Cotterill is expecting to add to his squad imminently.
"Relegation always affects a club, but at one stage last season I thought Portsmouth really looked like they were going to go up, although obviously the strength in depth wasn't there," added Varney. "But I know the manager is working hard in that area and hopefully I'll be one of a few good signings."